The Swans were handed their joint-highest Barclays Premier League defeat by Chelsea in a ruthless display by the leaders.
Oscar gave the visitors a perfect start at the Liberty as he fired low past Lukasz Fabianski after just 49 seconds.
Diego Costa doubled the lead after 20 minutes as he finished off a neat move involving Cesc Fabregas and Willian, who combined on the edge of the Swans box.
Two goals in three minutes then effectively ended the contest as Costa latched onto Federico Fernandez's pass intended for Fabianski and the striker slotted home from an acute angle.
The Liberty was stunned, and the celebrations had barely died down in the away end before Oscar curled a superb strike into the top corner to make it 4-0.
Chelsea also hit the woodwork twice through Willian, while Gylfi Sigurdsson's earlier effort had also clattered the post.
The second half proved a far quieter affair, though sub Andre Schurrle capped off a miserable day for the Swans as he tapped home the fifth goal with 11 minutes remaining.
This loss left the Swans on 30 points after 22 games.
The Swans made two changes to the starting XI.
Dutch international Dwight Tiendalli made his first league start of the season while Nelson Oliveira was also included in Garry Monk's starting XI for the first time since arriving on loan from Benfica.
The Swans were again without Jonjo Shelvey, who served the final game of his four-match suspension, and Jefferson Montero (hamstring) while Leon Britton missed out with a groin injury.
Ki Sung-Yueng was still unavailable due to his involvement in the Asian Cup. The Swans midfielder captained South Korea to a third straight win in the Asian Cup this morning against hosts Australia, with his nation progressing to the knockout stages.
Lukasz Fabianski, Dwight Tiendalli, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Tom Carroll, Gylfi Sigurdsson, Nelson Oliveira (Jay Fulton, 66), Nathan Dyer (Modou Barrow, 74), Wayne Routledge (Marvin Emnes, 32), Bafe Gomis.
Gerhard Tremmel, Angel Rangel, Jordi Amat, Kyle Bartley.
Petr Cech, Branislav Ivanovic, John Terry (capt), Gary Cahill, Filipe Luis, Eden Hazard, Nemanja Matic, Cesc Fabregas (Ramires, 74), Oscar, Willian (Andre Schurrle, 76), Diego Costa (Loic Remy, 74).
Thibaut Courtois, Kurt Zouma, John Obi Mikel, Mohamed Salah.
The visitors made a dream start at the Liberty as Oscar intercepted Gylfi Sigurdsson's pass - which had deflected off Tom Carroll - before firing low past Lukasz Fabianski after just 49 seconds.
Barely a minute later the Swans hit back, with Sigurdsson rattling the woodwork with a thunderous 25-yard effort which beat Petr Cech but not the post.
In a frenetic opening, Willian then wasted a good opportunity to double Chelsea's lead but he fired high and wide after Oscar's effort was parried by Fabianski.
Oscar was probing again soon after as Eden Hazard found him inside the box, but the Brazilian's low effort was driven wide.
There was no let up from the visitors either, with only a fine Fabianski save denying Hazard shortly after.
And with 20 minutes on the clock, they did double their lead.
Cesc Fabregas and Willian combined before Diego Costa coolly slotted home from 18 yards giving Fabianski no chance.
It could have got even worse for the hosts as Costa drove a powerful shot just over the crossbar just 60 seconds after his goal.
The Swans were on the backfoot, and a third almost arrived on the half-hour mark as Willian found himself in space in the box, but his drilled effort hammered back off the near post.
Garry Monk was forced into a change shortly after Wayne Routledge was replaced by Marvin Emnes after sustaining an injury.
Chelsea were simply ruthless, and they struck twice in three minutes to simply stun the Liberty.
Firstly, Costa took full advantage of Federico Fernandez's intended passback to Fabianski, with the striker converting from close range.
Then, Costa turned provider as he squared to Oscar, who curled a stunning effort into the top corner.
The Swans tried to cut the deficit when John Terry's headed clearance dropped to Sigurdsson, but he looped his half-volley wide from 20 yards.
But the break was brief, and the Blues went within inches of making matters even worse for the Swans as Costa raced on towards goal after collecting a loose ball, and when he rounded Fabianski, he teed up Willian, who thundered against the crossbar from 12 yards.
That proved the end of a disastrous first-half for the Swans, with Chelsea showing their ruthless streak in front of goal.
HALF-TIME: Swans 0 Chelsea 4
The action in the second half proved much different to that of the first.
Nelson Oliveira drove an effort wide for the Swans while, at the other end, Fabregas was denied by Fabianski.
Monk then made his second change as Jay Fulton replaced the Portuguese loanee with 24 minutes to go.
Fabianski again had to be alert to prevent Hazard from adding to the scoreline as he padded his goal-bound effort wide.
The final Swans change saw Modou Barrow replace Nathan Dyer for the remaining 15 minutes as the hosts went in search of a consolation
It proved the visitors, though, who went on to get the next goal.
Branislav Ivanovic worked his way into the box and his perfect cross allowed sub Andre Schurrle to tap in after 79 minutes.
That proved the end of a miserable afternoon for the Swans, who now prepare for next weekend's FA Cup trip to Blackburn.